Atributes Information

1. Fixed Acidity (tartaric acid - \(g/dm^3\) )
2. Volatile acidity (acetic acid - \(g/dm^3\) )
3. Citric acid (\(g/dm^3\) )
4. Residual sugar (\(g/dm^3\) )
5. Chlorides (sodium chloride - \(g/dm^3\) )
6. Free sulfur dioxide (\(mg/dm^3\) )
7. Total sulfur dioxide (\(mg/dm^3\) )
8. Density (\(g/cm^3\) )
9. pH
10. Sulphates (potassium sulphate - \(g/dm^3\))
11. Alcohol (% by volume)
12. Quality (score between 0 and 10)

Description Atributes

1. Fixed acidity: Most acids involved with wine or fixed or nonvolatile (do not evaporate readily)
2. Volatile acidity: The amount of acetic acid in wine
3. Citric acid: Found in small quantities, citric acid can add ‘freshness’ and flavor to wines
4. Residual sugar: The amount of sugar remaining after fermentation stops
5. Chlorides: the amount of salt in the wine
6. Free sulfur dioxide: The free form of SO2 exists in equilibrium between molecular SO2 (as a dissolved gas) and bisulfite ion; it prevents microbial growth and the oxidation of wine
7. Total sulfur dioxide: Amount of free and bound forms of S02; in low concentrations, SO2 is mostly undetectable in wine, but at free SO2 concentrations over 50 ppm, SO2 becomes evident in the nose and taste of wine
8. Density: The density of a substance is its mass per unite volume
9. pH: Describes how acidic or basic a substance is on a scale from 0 (very acidic) to 14 (very basic)
10. Sulphates: a wine additive which can contribute to sulfur dioxide gas (S02) levels, wich acts as an antimicrobial and antioxidant
11. Alcohol: The percent alcohol content of the wine
12. Quality: Score between 0 and 10

Fixed Acidity

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=fixed.acidity), binwidth = 0.5) +
  scale_x_continuous(breaks = seq(0,17,1)) +
  xlab("Fixed Acidity") +
  ylab("Count")

summary(wineData$fixed.acidity)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    4.60    7.10    7.90    8.32    9.20   15.90

The histogram is skewed right. The fixed acidity in most red wines is approximately between 6.5 \(g/dm^3\) and 7.5 \(g/dm^3\). The median (7.90) and mean (8.32) are pulled to the left, and tail is to the right, which are all indicators of a right skewed distribution.

Volatile Acidity

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=volatile.acidity), binwidth = 0.04) +
  scale_x_continuous(breaks = seq(0,1.6,0.1)) +
  xlab("Volatile Acidity") +
  ylab("Count")

summary(wineData$volatile.acidity)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.1200  0.3900  0.5200  0.5278  0.6400  1.5800

The histogram is skewed right. The volatile acidity in most red wines is approximately between 0.35 \(g/dm^3\) and 0.65 \(g/dm^3\). The median (0.52) and mean (≈ 0.53) are pulled to the left, and tail is to the right. There might be some outliers around 1.3 \(g/dm^3\) and 1.55 \(g/dm^3\).

Citric Acid

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=citric.acid), binwidth = 0.03) +
  scale_x_continuous(breaks = seq(0,1,0.125)) +
  xlab("Citric Acid") +
  ylab("Count")

summary(wineData$citric.acid)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.000   0.090   0.260   0.271   0.420   1.000

The histogram is skewed right. The citric acid in most red wines is approximately 0.0 \(g/dm^3\). The median (0.26) and mean (0.27) are pulled to the left.

Residual Sugar

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=residual.sugar), binwidth = 0.2) +
  xlim(1,7) +
  xlab("Residual Sugar") +
  ylab("Count")

## Warning: Removed 31 rows containing non-finite values (stat_bin).

summary(wineData$residual.sugar)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.900   1.900   2.200   2.539   2.600  15.500

The histogram is skewed right. The residual sugar in most red wines is approximately 2.0 \(g/dm^3\). The median (2.2) and mean (2.539) are pulled to the left. I also used xlim() to remove outliers to create a cleaner visual.

Chlorides

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=chlorides), binwidth = 0.01) +
  xlim(0,0.2) +
  xlab("Chlorides") +
  ylab("Count")

## Warning: Removed 41 rows containing non-finite values (stat_bin).

summary(wineData$chlorides)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## 0.01200 0.07000 0.07900 0.08747 0.09000 0.61100

The histogram is skewed right. The amount of chlorides found in most red wines is approximately 0.78 \(g/dm^3\). The median (0.79) and mean (≈ 0.087) are pulled to the left. I also used xlim() to remove outliers to create a cleaner visual.

Free Sulfur Dioxide

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=free.sulfur.dioxide), binwidth = 2) +
  scale_x_continuous(breaks = seq(0,70,5)) +
  xlab("Free Sulfur Dioxide") +
  ylab("Count")

summary(wineData$free.sulfur.dioxide)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    7.00   14.00   15.87   21.00   72.00

The histogram is skewed right. The citric acid in most red wines is approximately 6.0 \(mg/dm^3\). The median (14.0) and mean (15.87) are pulled to the left.

Total Sulfur Dioxide

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=total.sulfur.dioxide), binwidth = 5) +
  xlim(0,175) +
  xlab("Total Sulfur Dioxide") +
  ylab("Count")

## Warning: Removed 2 rows containing non-finite values (stat_bin).

summary(wineData$total.sulfur.dioxide)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    6.00   22.00   38.00   46.47   62.00  289.00

The histogram is skewed right. The amount of total sulfur dioxide found in most red wines is approximately 25.0 \(mg/dm^3\). The median (38.0) and mean (46.47) are pulled to the left. I also used xlim() to remove outliers to create a cleaner visual.

Density

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=density), binwidth = 0.0005) +
  scale_x_continuous(breaks = seq(0.9,1.05,0.0025)) +
  xlab("Density") +
  ylab("Count")

summary(wineData$density)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.9901  0.9956  0.9968  0.9967  0.9978  1.0037

The histogram is skewed right. The density of most red wines is approximately 0.996 \(g/cm^3\). The median (0.9968) and mean (0.9967) are pulled to the left.

pH

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=pH), binwidth = 0.05) +
  scale_x_continuous(breaks = seq(0,4,0.1)) +
  xlab("pH") +
  ylab("Count")

summary(wineData$pH)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   2.740   3.210   3.310   3.311   3.400   4.010

The histogram is skewed right. The pH of most red wines is approximately 3.3 pH units. The median (3.31) and mean (3.311) are pulled to the left.

Sulphates

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=sulphates), bandwidth = 0.25) +
  xlim(0.25, 1.5) +
  xlab("Sulphates") +
  ylab("Count")

## Warning: Ignoring unknown parameters: bandwidth

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 8 rows containing non-finite values (stat_bin).

## Warning: Removed 1 rows containing missing values (geom_bar).

summary(wineData$sulphates)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##  0.3300  0.5500  0.6200  0.6581  0.7300  2.0000

The histogram is skewed right. The amount of sulphatees found in most red wines is approximately 0.55 \(g/dm^3\). The median (0.62) and mean (≈ 0.65) are pulled to the left. I also used xlim() to remove outliers to create a cleaner visual.

Alcohol

ggplot(data = wineData) +
  geom_histogram(mapping = aes(x=alcohol), binwidth = 0.5) +
  scale_x_continuous(breaks = seq(8,15,1)) +
  xlab("Alcohol") +
  ylab("Count")

summary(wineData$alcohol)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    8.40    9.50   10.20   10.42   11.10   14.90

The histogram is skewed right. The amount of alcohol found in most red wines is approximately 8.0\(\%\) by volume. The median (10.2) and mean (10.42) are pulled to the left. I also used xlim() to remove outliers to create a cleaner visual.

Quality

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   3.000   5.000   6.000   5.636   6.000   8.000

The data set of red wine quality follows a normal distribution. Most wines are rated at a quality level of 5.0. When looking at other measures of central tendancy, the 1st quartile, median, 3rd quartile, and mean values are 5.0, 6.0, 6,0, and 5.636 respectively.

What is the structure of your dataset?

The data set contains 12 variables, 1599 rows.

What is/are the main feature(s) of interest in your dataset?

I am interested in looking at which ingredients drive quality ratings.

What other features in the dataset do you think will help support your investigation into your feature(s) of interest?

I would also like to investigate any corrleations found between acidity levels & pH, sulphates & density, or residual sugars & density.

Did you create any new variables from existing variables in the dataset?

No.

Of the features you investigated, were there any unusual distributions? Did you perform any operations on the data to tidy, adjust, or change the form of the data? If so, why did you do this?

No, I did not perform any operations on the dataset. But, I did reduce the xlim() max value on a few graphs to clean up the visualizations. Also regarding the quality graph, I’ve never seen a 2nd and 3rd quartile value equal the same value, found this to be interesting, and would like to dig into it further.

wineCorrelation <- cor(wineData)
significance <- cor.mtest(wineCorrelation, conf.level = .95)

corrplot(wineCorrelation, method = "number",
         p.mat = significance$p, sig.level = .05, insig = "blank", order="hclust", tl.col = "black",type="upper",tl.srt=45,
         col=brewer.pal(n=10,name="RdYlBu"))

head(round(wineCorrelation, 4))

##                     fixed.acidity volatile.acidity citric.acid
## fixed.acidity              1.0000          -0.2561      0.6717
## volatile.acidity          -0.2561           1.0000     -0.5525
## citric.acid                0.6717          -0.5525      1.0000
## residual.sugar             0.1148           0.0019      0.1436
## chlorides                  0.0937           0.0613      0.2038
## free.sulfur.dioxide       -0.1538          -0.0105     -0.0610
##                     residual.sugar chlorides free.sulfur.dioxide
## fixed.acidity               0.1148    0.0937             -0.1538
## volatile.acidity            0.0019    0.0613             -0.0105
## citric.acid                 0.1436    0.2038             -0.0610
## residual.sugar              1.0000    0.0556              0.1870
## chlorides                   0.0556    1.0000              0.0056
## free.sulfur.dioxide         0.1870    0.0056              1.0000
##                     total.sulfur.dioxide density      pH sulphates alcohol
## fixed.acidity                    -0.1132  0.6680 -0.6830    0.1830 -0.0617
## volatile.acidity                  0.0765  0.0220  0.2349   -0.2610 -0.2023
## citric.acid                       0.0355  0.3649 -0.5419    0.3128  0.1099
## residual.sugar                    0.2030  0.3553 -0.0857    0.0055  0.0421
## chlorides                         0.0474  0.2006 -0.2650    0.3713 -0.2211
## free.sulfur.dioxide               0.6677 -0.0219  0.0704    0.0517 -0.0694
##                     quality
## fixed.acidity        0.1241
## volatile.acidity    -0.3906
## citric.acid          0.2264
## residual.sugar       0.0137
## chlorides           -0.1289
## free.sulfur.dioxide -0.0507

set.seed(1599)
wine_subset <- wineData[,c(1:12)]
names(wine_subset)

##  [1] "fixed.acidity"        "volatile.acidity"     "citric.acid"         
##  [4] "residual.sugar"       "chlorides"            "free.sulfur.dioxide" 
##  [7] "total.sulfur.dioxide" "density"              "pH"                  
## [10] "sulphates"            "alcohol"              "quality"

ggpairs(wine_subset[sample.int(nrow(wine_subset), 1000),])

Bivariate Plots

Now that I looked at various matrices, I’ve determined which relationships I want to look at. Some items of interest are aclohol & quality, and fixed acidity & pH.

ggplot(data = wineData) +
  geom_bar(
    mapping = aes(x = round(alcohol), fill = factor(quality)),
    position = "dodge"
  )

ggplot(data = wineData, mapping = aes(x=alcohol, y=quality)) +
  geom_point(mapping = aes(color = factor(quality))) + 
  geom_smooth(color='red',method="lm")

round(cor(wineData$alcohol, wineData$quality), 2)

## [1] 0.48

Created grouped bar chart and scatter plot to look at alcohol and quality. There is a moderate positive correlation of approximately (0.48) between alcohol and quality.

round(cor(wineData$quality, wineData$total.sulfur.dioxide), 2)

## [1] -0.19

I created a jittering scatter plot to view the relationship between quality and total sulfur dioxide. The data looks to like it is normally distributed. It has a weak correlation of apporximately -0.19.

ggplot(data = wineData, mapping = aes(x=alcohol, y=density)) +
  geom_point(aes(position = "jitter", color="Density")) + 
  geom_smooth(method="lm")

## Warning: Ignoring unknown aesthetics: position

round(cor(wineData$alcohol, wineData$density), 2)

## [1] -0.5

This scatterplot looks at the relationship between alchol and density. As alcohol increases, density decreases. This inverse relationship has a moderate correlation of apporximately -0.5.

ggplot(data = wineData, mapping = aes(x=fixed.acidity, y=pH)) +
  geom_point(aes(position = "jitter"),color="blue") + 
  geom_smooth(color='red',method="lm")

## Warning: Ignoring unknown aesthetics: position

round(cor(wineData$fixed.acidity, wineData$pH), 2)

## [1] -0.68

Fixed acidity and pH also have an inverse relationship. As fixed acidity increases, pH decreases. The relationship has a strong correlation of apporximately -0.68.

ggplot(data = wineData, mapping = aes(x = citric.acid, y = pH)) +
  geom_point() + 
  geom_smooth(color='hotpink',method="lm")

round(cor(wineData$citric.acid, wineData$pH), 2)

## [1] -0.54

As citric acid increases, pH decreases. This is an inverse relationship, with a strong correlation of apporximately -0.54. This is similar to the previous graph.

ggplot(data = wineData, mapping = aes(x = citric.acid, y = volatile.acidity)) +
  geom_point() + 
  geom_smooth(color='orange',method="lm")

round(cor(wineData$citric.acid, wineData$volatile.acidity), 2)

## [1] -0.55

As citric acid increases, volatile acidity decreases. This is an inverse relationship, with a strong correlation of apporximately -0.55.

ggplot(data = wineData, mapping = aes(y=residual.sugar, x=alcohol)) +
  geom_point() + 
  geom_smooth(color='blue',method="lm")

round(cor(wineData$alcohol, wineData$residual.sugar), 2)

## [1] 0.04

The percent of alcohol and residual sugar have a very weak correlation of apporximately 0.04.

ggplot(data = wineData, mapping = aes(x=residual.sugar, y=density)) +
  geom_point() +
  geom_smooth(method = "lm")

round(cor(wineData$residual.sugar, wineData$density), 2)

## [1] 0.36

As residual sugar increases density tends to increase. The correlation of this relationship is apporximately 0.36, which is considered moderate.

ggplot(data = wineData, mapping = aes(x=fixed.acidity, y = density)) +
  geom_point(aes(position = "jitter", color="Density")) + 
  geom_smooth(method = "lm")

## Warning: Ignoring unknown aesthetics: position

round(cor(wineData$fixed.acidity, wineData$density), 2)

## [1] 0.67

There is a direct relationship between fixed acidity and density. As fixed acidity increases, density increases. The relationship has a strong correlation of apporximately 0.67.

ggplot(data = wineData, mapping = aes(x=fixed.acidity, y=citric.acid)) +
  geom_point() +
  geom_smooth(method = "lm")

round(cor(wineData$fixed.acidity, wineData$citric.acid), 2)

## [1] 0.67

Fixed acidity and citric acid also have a direct relationship. As fixed acidity increases, citric acid increases. The relationship has a strong correlation of apporximately 0.67. One question I have is whether citric acids also fall into the category of fixed acids?

ggplot(data = wineData, mapping = aes(x=chlorides, y=citric.acid)) +
  geom_point() +
  geom_smooth(method = "lm")

round(cor(wineData$chlorides, wineData$citric.acid), 2)

## [1] 0.2

There is a positive correlation between chlorides and citric acid. It is a weak correlation of apporximately -0.2.

ggplot(data = wineData, mapping = aes(x=free.sulfur.dioxide, y=total.sulfur.dioxide)) +
  geom_point(position = "jitter") +
  geom_smooth(method = "lm")

round(cor(wineData$free.sulfur.dioxide, wineData$total.sulfur.dioxide), 2)

## [1] 0.67

There is a direct relationship between free sulfur dioxide and total sulfur dioxide. As free sulfur dioxide increases, total sulfur dioxide increases. The relationship has a strong correlation of apporximately 0.67. This makes sense since free sulfur dioxide makes up the free forms of \(SO_2\) existing in total sulfar dioxide.

Talk about some of the relationships you observed in this part of the investigation. How did the feature(s) of interest vary with other features in the dataset?

I was most interested in alcohol and quality. My initial assumption was there would be a direct relationship between alcohol and quality. Although there was a moderate positive correlation (≈ 0.48), I thought the correlation would be stronger.

Did you observe any interesting relationships between the other features (not the main feature(s) of interest)?

The correlation between fixed acidity and pH is approximately -0.68. As fixed acidity increases, pH decreases. This makes sense considering the pH scale. Substances are considered more acidic as their pH approaches zero. I found it interesting that the pH range of wines in this study are equivalent to the pH of orange juice, soda, and acid rain.

I also thought it was interesting that there is not a strong relationship between percent of alcohol and residual sugar. My initial thought was wine with higher alcohol content had less sugar remaining. However, the trend shows little change in residual sugar as alcholol increases. This leads me to question how much sugar is placed into the various wines prior to fermintation? Could higher alcohol content receive higher amounts of sugar? Is there a formula to follow to acheive a desired alcohol level which leads to similar amounts of residual sugar?

What was the strongest relationship you found?

The strongest correlation I found exists between fixed acidity and pH (≈ -0.68).

Talk about some of the relationships you observed in this part of the investigation. Were there features that strengthened each other in terms of looking at your feature(s) of interest?

The scatterplot featuring citric acid, volatile acitidy, and quality shows that as citric acid increases, volatile acitidy tends to decrease, and quality tends to increase. While the scatterplot featuring fixed acidity, pH, and quality shows that as fixed acidity increases pH and quality tend to decrease.

The graphs featuring alcohol, density, and quality show that as alcohol content increases, density tends to decrease, and quality tends to increase. There is a weak correlation between density and quality (≈ -0.159), while there are moderate correlations in both alcohol & density (≈ -0.489), and alcohol & quality (≈ 0.472).

Were there any interesting or surprising interactions between features?

I had trouble finding a simple function that calculates r-squared. What I really wanted to do is place a regression line on a scatterplot and place the r-squared value on the graph.

I found it interesting that while some items increased others decreased (e.g. alcohol, density, and quality). I found some additional anomalies that are noted in the final plot section under plot three.

---

Plot One

ggplot(data = wineData, mapping = aes(x=residual.sugar, color=factor(quality))) +
  geom_histogram(binwidth = 0.2) +
  xlim(1,7) +
  xlab("Residual Sugar") +
  ylab("Count")

## Warning: Removed 31 rows containing non-finite values (stat_bin).

summary(wineData$residual.sugar)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   0.900   1.900   2.200   2.539   2.600  15.500

Description One

As stated in the univariate plot section, this histogram is skewed right. The residual sugar in most red wines is approximately 2.0 \(g/dm^3\). The median (2.2) and mean (2.539) are pulled to the left. I used xlim() to remove outliers to create a cleaner visual. This time, I also grouped the data by quality. Since quality followed a normal distribution in the univariate plot section, we can see the majority of wines recieved a quailty rating of 5 or 6. The color coding in this graph helps to uncover to uncover this.

Plot Two

ggplot(data = wineData, mapping = aes(x=alcohol)) +
  geom_point(aes(y=pH,color="pH")) +
  geom_point(aes(y=(density-.96)*100,color="Density")) +
  geom_smooth(aes(y=pH), color="#33CCCC", method = "lm") +
  geom_smooth(aes(y=(density-.96)*100), color="#FF6666", method = "lm") +
  scale_y_continuous(name="Density",sec.axis = sec_axis(~((./100)+.96), name="pH"))

Description Two

This graph displays two different relationships. A direct relationship between alcohol & density, and an inverse relationship between alcohol & pH. As alcohol increases, density decreases and pH increases. It can also be inferred that as pH increases, density decreases. This is also verified in the simple scatterplot matrix found in the bivariate plots section.

Throughout this entire project, I had the most fun working on this graph. The reason is I plotted a second variable (pH) along the vertical axis and it was not as simple as when working with software like excel. I had to use the scale_y_continuous() function which required a specific formula (i.e. ~((./100)+.96)) to scale the values for this axis to a desired set of numbers.

Plot Three

wineData$qualityBins = cut(wineData$alcohol,
                                 c(8:16))
ggplot(wineData, mapping = aes(x = factor(round(alcohol)), y = density)) +
  geom_boxplot(aes(fill = qualityBins))

Description Three

As stated in the multivariate plots section, as alcohol content increases, density tends to decrease, and quality tends to increase. I wanted to look at this data set using a different type of graph and chose a box plot. I noticed there are multiple dots below and above the min and max whiskers. I have never observed this before. I found out that some of these additional dots are outliers. Outliers should carefully be considered before being removed \(^4\). Outliers, lie 1.5 x IQR (interquartile range) below the 1st or above the 3rd quartile ranges. Running IQR() on pH provides one value for the entire range, and I could easily multiply this by 1.5. However, I believe I need to calculate multiple IQR values since I grouped data on citric.acid for this visualization. This is something I would like to research further.